You're able to play the KPA out of the CLR no problem, right? It's just recording with an interface that's giving you headaches, correct?
I haven't used your interface or DAW, but all I had to do was have one S/PDIF cable from the Kemper S/PDIF OUT to the interface S/PDIF IN.
After you hit the Kemper's Output button, on the right of the screen you'll see "SPDIF Output". Default is "Master Stereo." Unless you are doing some fancy reamping, just leave that as it is.
At this point, go into your interface's software, if any, and basically look around for anything you can set to S/PDIF. In my Focusrite MixControl software it's "Sync Source," which I set to S/PDIF.
At this point, go into your DAW and find "Options" or "Preferences" or whatever they call it in your case, and set your inputs to S/PDIF.
With your CLR hooked up to the Kemper's Main Outs you should be able to listen and record.
This is for recording the full rig you hear when playing normally. If you want to get the dry guitar signal, you'll need to follow those two reamping videos I posted in that other thread.